0 = 1?

[Anonymous No.12801740]

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ...
1/2 = 1/3 + 1/9 + 1/27 + ...
and each term has a similar construction where it can be represented by the sum of smaller numbers and so on.
thus 1 = lim n -> inf (1/n + 1/n + ...) = 0 + 0 + 0 + 0 +...
0 + 0 = 0
this 1 = 0.
However we're just making this assumption, it's a pretty standard assumption since we often use assumptions likes these with infinite series, we made it earlier claiming that the series of 1/2^n for n \in N >0 is 1.
However we can use hitomi density reasoning to make it reasonable.
As we should all know if you've ever browsed on /sci/ before Hitomi's number claims to be the most dense number such that induction or any standard arithmetic is arbitary when applied to it. The algebra isn't exactly closed, but its existence is all we need here.
the series 1/2^n as n increases 2^n becomes infinitely dense where it is now stuck in the Hitomi set and can now be considered a Hitomi number h. 1/h = 0 closing the series.
Thus we can claim the series is completely one.
so one can be rewritten as 1 = 1/h + 1/h + 1/h +...
well if the number that defines it's length is also h then h*1/h = 1.
And now we can all admit 0 * infinity is 1.
How can we pretend the delta function makes sense if this isn't true?
So I offer an amendment:
a completion of some sort.
That h*1/h only describes one and no other number.
One of the things we understand about Hitomi numbers is that by its existence regular arithmetic doesn't work very well on it.
h + 1 = h.
h plus infinitely dense amount of ones is h.
but this concept applies for any number infinitely dense number of 2s, 3s, ns.
so h + h = h thus 2h = h.
h*1/h only describes one.
If you want to merge the two algebras you need to accept the order.
2*{h*1/h} = 2
2 cannot merge with h*1/h because you're applying two different algebras.
One of infinities and one of definite numbers.

[Anonymous No.12801747]

is this the new /sg/ schizo general?

[Anonymous No.12801751]

[Anonymous No.12801765]

you know what's weird. you're told you can't multiply two vectors together. then are taught the vector definition of complex numbers.
But I can easily multiply two complex numbers together.
can someone explain this?
was I taught a far too informal understanding of complex numbers?

[Anonymous No.12801788]

>>12801765
vectors can't be multiplied in general. that doesn't mean there can't exist *some* vector spaces where multiplication is defined.

[Anonymous No.12801791]

>>12801788

[Anonymous No.12801888]

>>12801765
>>12801791

You can define multiplication on anything in math. The real question is, are there multiplicative inverses and does it obey distributivity with addition e.g. does a(b+c) = ab + ac. If not, it's probably not that useful. And if you insist that the result is always a vector, then it only really works in certain cases like with complex numbers, quaternions, and the octonions, etc. Although by the time you get to the octonions, you have to throw out associativity.

If you want to get something more general, you should look into Geometric Algebra. The TLDR is you can define any number of elements x,y, etc. whose square is 1, and then some element ax + by... is analogous to a k-dimensional vector. Then there's this thing called the "geometric product" which allows you to multiply vector's together, but the result is usually this thing called a bivector, which is sort of like a finite sized surface that is completed described by it's orientation and area. https://www.youtube.com/watch?v=60z_hpEAtD8

[Anonymous No.12801892]

>>12801740
good pic

[Anonymous No.12802015]

>>12801892
yeah I've just always thought it was interesting how people think they are the rebels despite the people who back them literally own and run the world.
also I wish I had a time machine so I could just watch dinosaurs all day.